Arturf is right. A better spreader is probably the answer to your uneven problem with granular fertilizer. Adjust it for even distribution. And calibrate it carefully.
Naturally, careful application is also important. I suggest measure out your swath width and place a marker at the proper distance to give you a target to shoot for. For example, place a tiny bit of shaving cream at exactly 8 foot intervals, across each end of the site.
Actually, a foaming hand soap is better, as it disappears more quickly.
A granular fertilizer designed especially for centipede is the best option. A soil test is a good idea--make sure your soil is not overly acidic.